Optical Cherenkov radiation in ultrafast cascaded second-harmonic generation

We show through theory and numerics that when few-cycle femtosecond solitons are generated through cascaded ( phase-mismatched) second-harmonic generation, these broadband solitons can emit optical Cherenkov radiation in the form of linear dispersive waves located in the red part of the spectrum. The beating between the dispersive wave and the soliton generates trailing temporal oscillations on the compressed soliton. Insertion of a simple short-wave pass filter after the crystal can restore a clean soliton. On the other hand, bandpass filtering around the dispersive wave peak results in near-transform-limited ultrashort mid-IR pulses with pulse durations much shorter than the input near-IR pulse. The Cherenkov radiation for the crystal considered (beta-barium borate) is found for pump wavelengths in the range lambda = 0.95-1.45 mu m, and is located in the regime lambda = 1.5-3.5 mu m. For shorter pump wavelengths, the phase-matching point is located in the absorption region of the crystal, effectively absorbing the generated dispersive wave. By calculating the phase-matching curves for typically used frequency conversion crystals, we point out that the mid-IR absorption in the crystal in many cases automatically will filter away the dispersive wave. Finally, an investigation of recent experimental results uncovers a four-wave-mixing phenomenon related to Cherenkov radiation that is an additional generation mechanism of long-wavelength radiation that can occur during soliton compression. We discuss the conditions that lead to this alternative dynamics rather than generation of Cherenkov radiation.